Question 86
In a $2n \times 2n$ grid exactly half of the squares have been coloured black and the other half are white. In one step one can take some $2 \times 2$ square in this grid and reflect its four squares w.r.t. the horizontal or vertical central axis. Which positive integers $n$ make it possible to get from any initial configuration to a state where the whole board has been coloured chessboard-style?